1. Divide the number repeatedly by 2:
Keep track of each remainder.
We stop when we get a quotient that is equal to zero.
- division = quotient + remainder;
- 111 000 011 045 ÷ 2 = 55 500 005 522 + 1;
- 55 500 005 522 ÷ 2 = 27 750 002 761 + 0;
- 27 750 002 761 ÷ 2 = 13 875 001 380 + 1;
- 13 875 001 380 ÷ 2 = 6 937 500 690 + 0;
- 6 937 500 690 ÷ 2 = 3 468 750 345 + 0;
- 3 468 750 345 ÷ 2 = 1 734 375 172 + 1;
- 1 734 375 172 ÷ 2 = 867 187 586 + 0;
- 867 187 586 ÷ 2 = 433 593 793 + 0;
- 433 593 793 ÷ 2 = 216 796 896 + 1;
- 216 796 896 ÷ 2 = 108 398 448 + 0;
- 108 398 448 ÷ 2 = 54 199 224 + 0;
- 54 199 224 ÷ 2 = 27 099 612 + 0;
- 27 099 612 ÷ 2 = 13 549 806 + 0;
- 13 549 806 ÷ 2 = 6 774 903 + 0;
- 6 774 903 ÷ 2 = 3 387 451 + 1;
- 3 387 451 ÷ 2 = 1 693 725 + 1;
- 1 693 725 ÷ 2 = 846 862 + 1;
- 846 862 ÷ 2 = 423 431 + 0;
- 423 431 ÷ 2 = 211 715 + 1;
- 211 715 ÷ 2 = 105 857 + 1;
- 105 857 ÷ 2 = 52 928 + 1;
- 52 928 ÷ 2 = 26 464 + 0;
- 26 464 ÷ 2 = 13 232 + 0;
- 13 232 ÷ 2 = 6 616 + 0;
- 6 616 ÷ 2 = 3 308 + 0;
- 3 308 ÷ 2 = 1 654 + 0;
- 1 654 ÷ 2 = 827 + 0;
- 827 ÷ 2 = 413 + 1;
- 413 ÷ 2 = 206 + 1;
- 206 ÷ 2 = 103 + 0;
- 103 ÷ 2 = 51 + 1;
- 51 ÷ 2 = 25 + 1;
- 25 ÷ 2 = 12 + 1;
- 12 ÷ 2 = 6 + 0;
- 6 ÷ 2 = 3 + 0;
- 3 ÷ 2 = 1 + 1;
- 1 ÷ 2 = 0 + 1;
2. Construct the base 2 representation of the positive number:
Take all the remainders starting from the bottom of the list constructed above.
111 000 011 045(10) = 1 1001 1101 1000 0001 1101 1100 0001 0010 0101(2)
3. Determine the signed binary number bit length:
The base 2 number's actual length, in bits: 37.
A signed binary's bit length must be equal to a power of 2, as of:
21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
The first bit (the leftmost) indicates the sign:
0 = positive integer number, 1 = negative integer number
The least number that is:
1) a power of 2
2) and is larger than the actual length, 37,
3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)
=== is: 64.
4. Get the positive binary computer representation on 64 bits (8 Bytes):
If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.
Number 111 000 011 045(10), a signed integer number (with sign), converted from decimal system (from base 10) and written as a signed binary in one's complement representation:
111 000 011 045(10) = 0000 0000 0000 0000 0000 0000 0001 1001 1101 1000 0001 1101 1100 0001 0010 0101
Spaces were used to group digits: for binary, by 4, for decimal, by 3.